Answer:
x=-85
Step-by-step explanation:
Answer:
(-3, 4)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
<u>Algebra I</u>
- Terms/Coefficients
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
y = -x + 1
2x + 3y = 6
<u>Step 2: Solve for </u><em><u>x</u></em>
<em>Substitution</em>
- Substitute in <em>y</em>: 2x + 3(-x + 1) = 6
- Distribute 3: 2x - 3x + 3 = 6
- Combine like terms: -x + 3 = 6
- Isolate <em>x</em> terms: -x = 3
- Isolate <em>x</em>: x = -3
<u>Step 3: Solve for </u><em><u>y</u></em>
- Define equation: y = -x + 1
- Substitute in <em>x</em>: y = -(-3) + 1
- Simplify: y = 3 + 1
- Add: y = 4
7 because you have to round 6 to 7 from the former seven and seven is bigger than 4 so the 6 would become a
7
Answer:
A. H(x) is an inverse of F(x)
Step-by-step explanation:
The given functions are:
![F(x)=\sqrt{x-2}](https://tex.z-dn.net/?f=F%28x%29%3D%5Csqrt%7Bx-2%7D)
![G(x)=(x-2)^2](https://tex.z-dn.net/?f=G%28x%29%3D%28x-2%29%5E2)
![H(x)=x^2+2](https://tex.z-dn.net/?f=H%28x%29%3Dx%5E2%2B2)
We compose F(x) and G(x) to get:
![(F\circ G)(x)=F(G(x))](https://tex.z-dn.net/?f=%28F%5Ccirc%20G%29%28x%29%3DF%28G%28x%29%29)
![(F\circ G)(x)=F((x-2)^2)](https://tex.z-dn.net/?f=%28F%5Ccirc%20G%29%28x%29%3DF%28%28x-2%29%5E2%29)
![(F\circ G)(x)=\sqrt{(x-2)^2-2}](https://tex.z-dn.net/?f=%28F%5Ccirc%20G%29%28x%29%3D%5Csqrt%7B%28x-2%29%5E2-2%7D)
![(F\circ G)(x)=\sqrt{x^2-4x+4-2}](https://tex.z-dn.net/?f=%28F%5Ccirc%20G%29%28x%29%3D%5Csqrt%7Bx%5E2-4x%2B4-2%7D)
![(F\circ G)(x)=\sqrt{x^2-4x+2}](https://tex.z-dn.net/?f=%28F%5Ccirc%20G%29%28x%29%3D%5Csqrt%7Bx%5E2-4x%2B2%7D)
![(F\circ G)(x)\ne x](https://tex.z-dn.net/?f=%28F%5Ccirc%20G%29%28x%29%5Cne%20x)
Hence G(x) is not an inverse of F(x).
We now compose H(x) and G(x).
![(F\circ H)(x)=F(H(x))](https://tex.z-dn.net/?f=%28F%5Ccirc%20H%29%28x%29%3DF%28H%28x%29%29)
![(F\circ H)(x)=F(x^2+2)](https://tex.z-dn.net/?f=%28F%5Ccirc%20H%29%28x%29%3DF%28x%5E2%2B2%29)
![(F\circ H)(x)=\sqrt{x^2+2-2}](https://tex.z-dn.net/?f=%28F%5Ccirc%20H%29%28x%29%3D%5Csqrt%7Bx%5E2%2B2-2%7D)
We simplify to get:
![(F\circ H)(x)=\sqrt{x^2}](https://tex.z-dn.net/?f=%28F%5Ccirc%20H%29%28x%29%3D%5Csqrt%7Bx%5E2%7D)
![(F\circ H)(x)=x](https://tex.z-dn.net/?f=%28F%5Ccirc%20H%29%28x%29%3Dx)
Since
, H(x) is an inverse of F(x)